Put The Following Equation Of A Line Into Slope-intercept Form (fractions If Necessary).$2x + 4y = 16$

Introduction

In mathematics, the slope-intercept form of a linear equation is a fundamental concept that helps us understand the relationship between the variables in a linear equation. The slope-intercept form is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will learn how to convert the given equation of a line into slope-intercept form, using fractions if necessary.

Understanding the Given Equation

The given equation of a line is $2x + 4y = 16$. To convert this equation into slope-intercept form, we need to isolate the variable y. The first step is to subtract 2x from both sides of the equation, which gives us $4y = -2x + 16$.

Isolating the Variable y

To isolate the variable y, we need to divide both sides of the equation by 4. This gives us $y = \frac{-2x}{4} + \frac{16}{4}$.

Simplifying the Equation

We can simplify the equation by dividing the numerator and denominator of the fractions by their greatest common divisor, which is 2. This gives us $y = \frac{-x}{2} + 4$.

Conclusion

In this article, we learned how to convert the given equation of a line into slope-intercept form, using fractions if necessary. We started by subtracting 2x from both sides of the equation, then divided both sides by 4 to isolate the variable y. Finally, we simplified the equation by dividing the numerator and denominator of the fractions by their greatest common divisor. The resulting equation is $y = \frac{-x}{2} + 4$, which is in slope-intercept form.

Example Problems

Problem 1

Convert the equation $3x + 2y = 12$ into slope-intercept form.

Solution

To convert the equation into slope-intercept form, we need to isolate the variable y. The first step is to subtract 3x from both sides of the equation, which gives us $2y = -3x + 12$. Then, we divide both sides of the equation by 2, which gives us $y = \frac{-3x}{2} + 6$.

Problem 2

Convert the equation $x + 5y = 15$ into slope-intercept form.

Solution

To convert the equation into slope-intercept form, we need to isolate the variable y. The first step is to subtract x from both sides of the equation, which gives us $5y = -x + 15$. Then, we divide both sides of the equation by 5, which gives us $y = \frac{-x}{5} + 3$.

Tips and Tricks

• When converting an equation into slope-intercept form, make sure to isolate the variable y.
• Use fractions if necessary to simplify the equation.
• Divide the numerator and denominator of the fractions by their greatest common divisor to simplify the equation.

Common Mistakes

• Failing to isolate the variable y.
• Not using fractions when necessary.
• Not simplifying the equation by dividing the numerator and denominator of the fractions by their greatest common divisor.

Conclusion

Introduction

In our previous article, we learned how to convert the given equation of a line into slope-intercept form, using fractions if necessary. In this article, we will answer some frequently asked questions about converting linear equations into slope-intercept form.

Q&A

Q1: What is the slope-intercept form of a linear equation?

A1: The slope-intercept form of a linear equation is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

Q2: How do I convert a linear equation into slope-intercept form?

A2: To convert a linear equation into slope-intercept form, you need to isolate the variable y. This can be done by subtracting the x-term from both sides of the equation, then dividing both sides by the coefficient of y.

Q3: What if the equation has a fraction as the coefficient of y?

A3: If the equation has a fraction as the coefficient of y, you can simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Q4: Can I use a calculator to convert a linear equation into slope-intercept form?

A4: While a calculator can be helpful in simplifying fractions, it is not necessary to use a calculator to convert a linear equation into slope-intercept form. You can do it manually by following the steps outlined above.

Q5: What if the equation has a negative sign in front of the x-term?

A5: If the equation has a negative sign in front of the x-term, you can simply move the negative sign to the other side of the equation by changing the sign of the x-term.

Q6: Can I convert a linear equation into slope-intercept form if it has a variable on both sides of the equation?

A6: Yes, you can convert a linear equation into slope-intercept form even if it has a variable on both sides of the equation. You just need to isolate the variable y by subtracting the x-term from both sides of the equation, then dividing both sides by the coefficient of y.

Q7: What if the equation has a fraction as the constant term?

A7: If the equation has a fraction as the constant term, you can simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Q8: Can I use a graphing calculator to convert a linear equation into slope-intercept form?

A8: While a graphing calculator can be helpful in visualizing the graph of a linear equation, it is not necessary to use a graphing calculator to convert a linear equation into slope-intercept form. You can do it manually by following the steps outlined above.

Tips and Tricks

• Make sure to isolate the variable y when converting a linear equation into slope-intercept form.
• Use fractions if necessary to simplify the equation.
• Divide the numerator and denominator of the fractions by their greatest common divisor to simplify the equation.
• Be careful when moving negative signs to the other side of the equation.

Common Mistakes

• Failing to isolate the variable y.
• Not using fractions when necessary.
• Not simplifying the equation by dividing the numerator and denominator of the fractions by their greatest common divisor.
• Moving negative signs incorrectly.

Conclusion

In this article, we answered some frequently asked questions about converting linear equations into slope-intercept form. We hope that this article has been helpful in clarifying any doubts you may have had about this concept. Remember to isolate the variable y, use fractions when necessary, and simplify the equation by dividing the numerator and denominator of the fractions by their greatest common divisor. With practice and patience, you will become proficient in converting linear equations into slope-intercept form.